The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X  1  1  1  X  X  X  X  X  X  X  1  1  1
 0  X  0  X 2X 2X  0  X 2X 4X 4X 2X 4X  0  X 4X  0  X 2X 4X 3X 3X 3X 3X 3X  0  0  X  X 2X 4X  0 2X  X 4X 2X 2X 4X 4X 3X  X  0  X 2X  X  X  0 4X 2X 2X  X  0 2X 4X 4X 3X 3X 3X
 0  0  X 3X 2X 3X 2X  X  X 3X  0 4X 4X 4X 2X  X 3X 4X  0 2X  0  X 2X 4X 3X  0  X 3X 4X 4X  0 3X  X  0 4X 2X 3X 3X  X  X  X 2X 2X  0 4X  X 4X 2X  0  X 2X  X 4X 2X 4X  0 2X 4X

generates a code of length 58 over Z5[X]/(X^2) who´s minimum homogenous weight is 226.

Homogenous weight enumerator: w(x)=1x^0+160x^226+48x^230+180x^231+60x^235+60x^236+12x^240+100x^241+4x^245

The gray image is a linear code over GF(5) with n=290, k=4 and d=226.
This code was found by Heurico 1.16 in 0.0715 seconds.